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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On commuting families of nonexpansive operators


Author: Gideon Schechtman
Journal: Proc. Amer. Math. Soc. 84 (1982), 373-376
MSC: Primary 47H09; Secondary 47H10
MathSciNet review: 640234
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Abstract: For each $ n$, $ 1 \leqslant n \leqslant \infty $, there exist a weakly compact, convex subset $ W$ of $ {L_1}$ and a family $ \{ {T_i}\} _{i = 1}^n(\{ {T_i}\} _{i = 1}^\infty {\text{ in case }}n = \infty )$ of nonexpansive operators of $ W$ into $ W$ such that there is no common fixed point for the whole family but any (finite) strict subfamily admits a common fixed point.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0640234-3
PII: S 0002-9939(1982)0640234-3
Keywords: Common fixed point, nonexpansive operators, weakly compact sets, convex sets
Article copyright: © Copyright 1982 American Mathematical Society